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tconometrics

WARNING: The theoretical mathematical models herein are for educational purposes only. This is not financial advice. Trading can get you REKT very quickly. Only do it if you know what you are doing and have fully comprehended all of the tax and legal obligations and sought the advice of a licensed financial advisor.

Introduction


Scientific method is difficult for most to comprehend. It is counterintuitive. It can lead to conclusions that do not reflect personal beliefs. It takes a foundation in the method to understand this basic fundamental concept: it is ok to be wrong. This should be something that is taught in school. If we are afraid of getting it wrong, we will never propose anything new.

The history of scientific discovery is therefore by its’ very nature surrounded in serendipity. Things that people discover by accident can be just as important as (or more important than) whatever it is they originally set out to do. Their original ideas might have been incorrect or inconclusive, but the things they discovered on the journey built the framework for those who follow.

According to the great modern scientific philosopher Karl Popper, testing a hypothesis for an incorrect outcome is the only reliable way to add weight to the argument that it is correct. If rigorous and repeated tests cannot show that a hypothesis is incorrect, then with each test the hypothesis assumes a higher likelihood of being correct. This concept is called Falsifiability.

Bitcoin RoPE


RoPE stands for Robust Probability Estimator. How is it “robust” exactly? It is robust strictly in the statistical sense — it is non parametric. Parametric methods are based on statistical distributions, like the Normal distribution for instance. These distributions are described by functions and the functions have parameters. For example, the “standard” normal distribution has the parameters mean of 0, variance of 1 (tip: you might see this as ~N(0,1)). A “non” parametric method does not rely on distributions or distributional assumptions (to an extent!), and such does not rely on varying the parameters to any distribution. Log Returns implies that an action is taken, here we have replaced this language with the more appropriate “log-deltas” i.e. the first differences of the log of the daily close prices. The rope can only stretch so far before it snaps taut and the delta comes back to it. Remember — the log deltas are essentially the percentage returns. This indicator thus gives you the capacity to estimate the risk of holding through a high return, or selling during a low one.

more information here.

Geometric Brownian Motion Monte Carlo Simulation


Think of a helium baloon that’s been released. The baloons general direction is going to be “up” — this is what we would call the drift. On it’s way up to the moon, there will be shocks (in any direction, down, up, sideways — whatever!). The shocks to the flight of the baloon are what we would call volatility. What we are doing here is releasing 10 thousand “pretend” baloons at once and studying their movement, so that we can make a prediction about what will happen when we release the real one. This approach completely removes any reliance on memes, narratives or emotion (or for that matter expectations on human action). The only assumptions are evidenced by history — the drift and the volatility. The model can be recalculated at any time and the predictions can be refined.

more information here.

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